THE MORPHOLOGY OF TOURNAMENTS

Given a directed graph G = (V, E), a subset X of V is an interval of G when for a, b is an element of X and x is an element of V - X, (a, x) is an element of E (resp. (x, a) is an element of E) if and only if ( b, x) is an element of E (resp. (x, b) is an element of E). With each h greater than or equal to 0 is associated the tournament T-h = ({0, . .., 2h}, {(i, j)/j - i is an element of {1, ..., h} modulo 2h + 1}). I n this Note, for all the integers h and n, we introduce the family C-h ,C- n of tournaments T defined on {0, ..., 2h + n} and fulfilling: T({ 0, ..., 2h}) = T-h and {0, ..., 2h} is an interval of T. We next consi der the class F-h,F- n of finite tournaments satisfying: T does not em bed the elements of C-h,C- n, however for every S is an element of C-h ,C- n, if X is a proper subset of {0, ..., 2h + n}, then T embeds S(X) . Using the characterization of tournaments of F-1,F- 1, we examine th e morphology of tournaments of F-1,F- 2.